| 摘要: |
| 设素数p≥3,对模p的任一原根x,且1≤x<p,一定存在模p的唯一的原根x且1≤x<p,使得xx≡1(modp).若x与x具有相反的奇偶性,则x就称为Lehmer DH数.本文利用广义Kloostermann和估计与三角和估计研究模p剩余系中Lehmer DH数与其逆之差的分布. |
| 关键词: LehmerDH数 分布性质 原根 广义Kloostermann和 渐近公式 |
| DOI： |
| 投稿时间：2002-05-08 |
| 基金项目:陕西省教委专项科研基金资助项目(00JK123)。 |
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| On the Distribution Property of Lehmer DH Number |
|
Gao Li
|
| (College of Math. & Comp. Sci., Yan'an University, Yan'an, Shaanxi, 716000, China) |
| Abstract: |
| Let p ≥ 3 be a prime,for each primitive root x modulo p with 1 ≤ x<p, it is clear that there exists one and only one primitive roor x modulo p with 1 ≤ x<p such that xx≡1(mod p).The number x is called as Lehmer DH mumber if x and x are of opposite parity. This p aper is to study the distribution property of Lehmer DH number by using the estimation of general Kloostermann sum and trigonometric sum. |
| Key words: Lehmer DH number distribution property primitive root kloostermann sum asymptotic formula |
